Final answer:
The Metropolitan Opera, NBC Symphony Orchestra, and CBS Orchestra are the organizations that broadcast weekly performances nationally in the early twentieth century. The San Antonio Opera did not partake in such early national broadcasts.
Step-by-step explanation:
The organizations that broadcast weekly performances for a nationwide audience in the early twentieth century include the Metropolitan Opera, the NBC Symphony Orchestra, and the CBS Orchestra. The Metropolitan Opera began broadcasting live radio performances to the nation in December 1931, becoming a Saturday afternoon staple for many across the country.
The NBC Symphony Orchestra was created by the network in 1937 specifically for radio broadcasts, which featured the famed conductor Arturo Toscanini. The CBS Orchestra also provided nationwide music broadcasts. In contrast, the San Antonio Opera is not known for such early broadcast activities on a national level.
During these broadcasts, listeners could enjoy a variety of entertainment, from classical music to comedy programs, plays, and news. Therefore, only the first three mentioned organizations were major players in the early broadcast landscape, reaching millions of households.